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Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method

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  • Jacod, Jean
  • Mykland, Per A.

Abstract

This paper introduces adaptiveness to the non-parametric estimation of volatility in high frequency data. We consider general continuous Itô processes contaminated by microstructure noise. In the context of pre-averaging, we show that this device gives rise to estimators that are within 7% of the commonly conjectured “quasi-lower bound” for asymptotic efficiency. The asymptotic variance is of the form constant × bound, where the constant does not depend on the process to be estimated. The results hold with mild assumptions on the noise, and extend to mildly irregular observations.

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  • Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:2910-2936
    DOI: 10.1016/j.spa.2015.02.005
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    Cited by:

    1. Altmeyer, Randolf & Bibinger, Markus, 2015. "Functional stable limit theorems for quasi-efficient spectral covolatility estimators," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4556-4600.
    2. Richard Y. Chen, 2018. "Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise," Papers 1810.04725, arXiv.org, revised Nov 2019.
    3. Clinet, Simon & Potiron, Yoann, 2018. "Efficient asymptotic variance reduction when estimating volatility in high frequency data," Journal of Econometrics, Elsevier, vol. 206(1), pages 103-142.
    4. Vladimír Holý & Petra Tomanová, 2023. "Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Data," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 463-485, June.
    5. Li, M. Z. & Linton, O., 2021. "Robust Estimation of Integrated and Spot Volatility," Cambridge Working Papers in Economics 2115, Faculty of Economics, University of Cambridge.
    6. Jean Jacod, 2019. "Estimation of volatility in a high-frequency setting: a short review," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 351-385, December.
    7. Li, Z. Merrick & Laeven, Roger J.A. & Vellekoop, Michel H., 2020. "Dependent microstructure noise and integrated volatility estimation from high-frequency data," Journal of Econometrics, Elsevier, vol. 215(2), pages 536-558.
    8. Ikeda, Shin S., 2016. "A bias-corrected estimator of the covariation matrix of multiple security prices when both microstructure effects and sampling durations are persistent and endogenous," Journal of Econometrics, Elsevier, vol. 193(1), pages 203-214.
    9. Zhang, Chuanhai & Liu, Zhi & Liu, Qiang, 2021. "Jumps at ultra-high frequency: Evidence from the Chinese stock market," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    10. Vladim'ir Hol'y & Petra Tomanov'a, 2020. "Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Data," Papers 2003.13062, arXiv.org, revised Dec 2021.
    11. Altmeyer, Randolf, 2023. "Central limit theorems for discretized occupation time functionals," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 101-125.

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